By the late 1700's, the apothecary run by the creole Antione Amadie Peychaud was doing brisk business. From his shop on Royal Street, Peychaud treated stomach ailments with his unique mixture of brandy and his own bitters that he served it in a French egg cup called a coquetier. The Yankees with belly aches mispronounced as "cocktail."
Whatever they called it, it was a hit. Soon the cocktail was being served all over town, and in 1853 the Sazerac Coffee House was making it's brandy toddy with Sazerac de Forge et fils cognac. Sometime around 1870 The Sazerac tweeked the recipe, dropping the expensive brandy it was named after and replacing it with American rye whiskey, and adding a dash of the wildly popular absinthe. Because, why not?
No one seemed to minds, because by 1872, the Sazarac had 18 bartenders manning a 125 foot bar churning them out. To wit:
One jigger Rye Whiskey (or use the original brandy it's lovely)
Sugar cube, crushed
3 dashes Peychaud's bitters
2 dashes Angostura bitters
Chill in a shaker with crushed ice, strain into glass laced with absinthe. Garnish with a lemon twist.